I X ( 

 Cor. 1. When the power acts parallel to the plan*,, 



p : w :: H : L. 

 p : p :: H : B. 

 P : w :: B : L. 



Cor. 2. When the power nets parallel to the ba**, 



p : w :: H : B. 

 p : p :: H : L 



P : w :: L : B. 



i 



Cor. 3. If W and a be invariable, P varies as 



P is least, 



sin. /3 * 



when it acts in the direction of the plane ; and is indefinitely great, 

 when it acts perpendicular to the plane. 



Cor. 4. If P and he invariable, W varies as sin. j3 ; .". W is the great- 

 est, when P acts in the direction of the plane, and the least when P acts 

 perpendicular to the plane. 



Cor. 5. If P and at, be given, p varies as sin. y, and .*. is the greatest 

 when P acts parallel to the base. 



Cor. 6. If two weights P and W sustain each other on two planes, 

 whose lengths are L and 1, and which have a common altitude by means 

 of a string passing over a pulley fixed at the intersection of the planes, 



p : w :: L : A 



Cor. 7. If the pulley be above the in- 

 tersection of the planes, as in the an- 

 nexed figure, 



p : w :: sin. B c A x cos. D p A 



: sin. A B C X cos. D W A. 



Cor. 8. If a string fixed at A pass round 

 the weight W, and then be parallel to the 

 plane, 



p : w :: i H : L. 



146 



